physical vs mathematical spacetime

[AntonioLao]

Physical spacetime is simply described by squares of energy. In a simplest description, a point of mathematical spacetime is described by a given point in a Feynman diagram of a two dimensional coordinate’s plane where the prescribed horizontal coordinate line axis represents the one dimensional space and the vertical axis represents the passage of time. Each spacetime event is then represented by a pair of ordered numbers: (x,t) where x and t are, respectively, the space and time distances measured from the spacetime origin at (0,0). For quantized spacetime events both x and t take integer values: 1, 2, 3, …, all the way to positive infinity. Since negative integers are well defined, spacetime events can also take values of -1, -2, -3, …, all the way to negative infinity. However, for continuous spacetime events the pair (x,t) must be composed of real numbers besides the integers. Furthermore, real numbers are constructed from all points found along the real number line representing both rational as well as irrational numbers. Nevertheless, the pair of numbers (x,t) cannot be both represented by irrationals: the number pi, Euler’s number, or the square root of non-perfect squares. The problem of measurability arises whenever time is represented by an irrational number. Therefore, physical laws are only meaningful if and only if the time takes on at the least integer values and at most rational numbers.